Higher Order Layer Resolving Numerical Scheme For Singularly Perturbed Boundary Turning Point Problems

Abstract

In this thesis, higher-order layer resolving numerical scheme is presented for singularly perturbed boundary turning point problems. The method is attempted on piecewise uniform mesh of the shishkin mesh type. The discrete problem is transformed in to linear systems of algebraic equations. That can be solved using Thomas algorithm. To validate the applicability of the proposed method, some model examples have been considered and solved for different values of perturbation parameter and mesh sizes. Both the theoretical investigation and numerical illustration have been confirmed for the method. As it can be observed from the numerical results presented in tables and graphs, the present method approximate the exact solution very well. Moreover, the present method give better results than some existing numerical methods reported in the literature.